On Exponential Sums in Finite Fields, II.
On extremal additive codes of length to
In this paper we consider the extremal even self-dual -additive codes. We give a complete classification for length . Under the hypothesis that at least two minimal words have the same support, we classify the codes of length and we show that in length such a code is equivalent to the unique -hermitian code with parameters [18,9,8]. We construct with the help of them some extremal -modular lattices.
On Fail-Rolle polynomials with few roots.
On Fully Split Lacunary Polynomials in Finite Fields
We estimate the number of possible degree patterns of k-lacunary polynomials of degree t < p which split completely modulo p. The result is based on a combination of a bound on the number of zeros of lacunary polynomials with some graph theory arguments.
On fundamental sets over a finite field.
On generalized Redei functions.
On linear recursion and pseudorandomness
On orthogonal systems and permutation polynomials in several variables
On partitions and cyclotomic polynomials.
On perfect polynomials over .
On permutation polynomials over finite fields.
On polynomial Gauss sums (mod Pⁿ), n ≥ 2
On polynomials of the form .
On rationality of Jacobi sums
On real quadratic number fields suitable for cryptography.
On sets of polynomials whose difference set contains no squares
Let be the polynomial ring over the finite field , and let be the subset of containing all polynomials of degree strictly less than N. Define D(N) to be the maximal cardinality of a set for which A-A contains no squares of polynomials. By combining the polynomial Hardy-Littlewood circle method with the density increment technology developed by Pintz, Steiger and Szemerédi, we prove that .
On singular moduli for rank 2 Drinfeld modules
On solutions of polynomial congruences
On Solvability by Radicals of Field Extensions.
On Solvability by Radicals of Finite Fields.